# The `log1pl` function
The **`log1pl`** function takes a `long double` argument (`arg`) and computes `ln(1 + arg)`.

The `log1pl` function is defined in the `math.h` standard library with the following structure:
```c
long double log1pl( long double arg );
```

> Note: The `log1pl(arg)` function is more precise than `logl(1 + arg)` if `arg` is closer to zero.

# Parameters
- `arg`: a `long double` number

# Return value
- If no errors occur, then `ln(1 + arg)` is returned.
- If `arg` is positive or negative zero, then `arg` is returned.
- If a domain error occurs (e.g., where `1 + arg` is less than `0`), `NaN` is returned.
- If a pole error occurs (e.g., result of `ln(1 + arg)` is infinity), $-\infty$ is returned.
- If `arg` is $+\infty$, $+\infty$ is returned.
- If `arg` is `NaN`, then `NaN` is returned.

# Example usage of the `log1pf` function
The following code provides a comparison between the `log1pl` and `logl` functions: 

#include<stdio.h>
#include<math.h>
#include<float.h>
int main() {
  long double x = 1e-20;
  long double y = 1 + x;

  printf("log1pl(1e-20) = %Lg\n", log1pl(x));
  printf("logl(1 + 1e-20) = %Lg\n", logl(y));
}

gcc compiler

In the example above, both functions compute `ln(1 + e^(-20))`, but `log1pl` gives a non-zero result. Therefore, `log1pl` must be used if the argument `arg` is close to zero since the result has higher precision.

The following code demonstrates the corner case inputs to the `logpf` function:

#include<stdio.h>
#include<math.h>
#include<float.h>
int main() {
  printf("log1pl(+0.0) = %Lf\n", log1pl(+0.0));
  printf("log1pl(-0.0) = %Lf\n", log1pl(-0.0));
  printf("log1pl(+inf) = %Lf\n", log1pl(INFINITY));
  printf("log1pl(-1.0) = %Lf\n", log1pl(-1.0));
}

gcc.tar.gz

What are some edge cases of log1pl?

Handles long double arguments to compute ln(1 + arg), providing more precision near zero. Returns NaN, infinity, or errors based on input.

What are some edge cases of log1pl?

The log1pl function

Parameters

Return value

Example usage of the log1pf function

The `log1pl` function

Example usage of the `log1pf` function